Happy Birthday, Johannes Kepler!

Johannes Kepler (December 27, 1571- November 15, 1630) solved the major problems of the Copernican system with his three laws of planetary motion. He was also a great geometer, as indicated by his trapezoidal beard.

Johannes Kepler was born on this date in 1571. A contemporary of Galileo and an assistant to Tycho, Kepler managed to solve the problems inherent in both their systems, making the heliocentric model Copernicus developed into something like the view we hold today. In Copernicus’ model, the Sun is the center of the Solar System, but the orbits of planets are circular, with smaller circles to correct for the fact that planets vary in their distances from the Sun. Galileo’s model was worse: he ignored the data and held that planetary orbits were precisely circular, which just doesn’t work.

Tycho didn’t like the Copernican model, but being a good scientist (despite also being nuts) he couldn’t blithely accept the old geocentric model either. As a result, the Tycho model is a hybrid: the Sun and Moon orbit Earth, while the planets orbit the Sun. As with the old geocentrists, he wasn’t entirely misguided in his thinking: after all, if the stars don’t orbit Earth, they would exhibit parallax, they must be very far away, and must also be very large. We know today that most stars we see in the night sky are very large and far away, so we may forgive Tycho at least some of his errors.

Elliptical orbit of a planet around the Sun. Note that the Sun isn't at the center of the ellipse but at a special point called a focus. I've exaggerated how eccentric the orbit is for clarity; planets in our Solar System follow paths that are closer to being circular.

Kepler used Tycho’s excellent observational data to create a major improvement on the Copernican system, in the form of his three laws of planetary motion:

All planets orbit the Sun along elliptical paths, with the Sun at one focus. Earth is itself a planet in this system. (For more about this, see my earlier post about Kepler-22b.)

Planets near the aphelion (the farthest point from the Sun in the orbit) move more slowly than planets near the perihelion (the closest approach to the Sun), so that an equal area of the orbit is swept out in equal times by an imaginary line connecting the planet with the Sun. Today we understand this law using physics, but Kepler obtained it by observation.

The time it takes a planet to orbit the Sun is related to how large its orbit is, by a relatively simple relation:where M is the mass of the Sun (equal to 1 in Kepler’s units), P is the period of orbit in Earth years, and a is the average distance to the Sun in astronomical units (equal to 1 for Earth). Again, we can find this relation using physics, but Isaac Newton’s work came after Kepler’s death.

Kepler was a man of his time, so his work isn’t free of what we would call pseudoscience today. He was fond of the idea that planets follow a neat mathematical pattern in their distances from the Sun, which kind of works for some planets but breaks down the farther out you go. He attempted to associate planetary orbits with musical notes (akin to the “music of the spheres” metaphor seen elsewhere), but again nature doesn’t follow patterns quite so neat. He even worked as an astrologer, which was fairly normal for the time. However, I don’t believe in condemning someone based on today’s knowledge, so I don’t hold any of that against him.

Isaac Newton’s birthday is December 25, which I didn’t commemorate since, well, it was Christmas and I wasn’t working. Newton showed why Kepler’s laws worked, based on his new laws of gravitation and motion, ultimately putting all of astronomy into the realm of physics where they had previously been separate. We should still honor Kepler, though: he discovered how the planets move without the benefit of Newton’s mechanics, which is a rather amazing feat. Happy 440th birthday, Johannes Kepler. Everyone go outside tonight and look at some planets in his honor.

In the introduction to Astronomia Nova 1609 Kepler states that the planetary orbits round the Sun are elliptical and that the velocity of the planets is inversely related to their distance from the Sun. Kepler gives greater mathematical precision to these comments and also the important concept of the foci in his later works. It has taken a long time for Kepler’s laws to be accepted and also Galileo’s, largely because of religious prohibition of the reading of their works, also Newton’s Principia represents a gross distortion of their works.